Solve \(dy/dx=2x\).

Solve \(dy/dx=xy\).

Solve \(dy/dx=y^2\).

Solve the initial value problem \(dy/dx=3y\), \(y(0)=4\).

Solve \(dy/dx=x(1+y^2)\).

Solve \(dy/dx=(x^2)/(y)\), assuming \(y\ne0\).

Solve \(dy/dx=e^x e^{-y}\).

Solve the logistic equation \(dy/dt=y(1-y)\) for \(0<y<1\).

Solve \(dy/dx=\frac{x+1}{y+2}\), assuming \(y\ne-2\).

Solve the initial value problem \(dy/dx=x/y\), \(y(0)=2\), assuming \(y>0\).